Chapter 9 Unit Question – How do we solve linear systems?

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Presentation transcript:

Chapter 9 Unit Question – How do we solve linear systems?

Open Learning Logs Date on Left…Section 9 – 3 on right

WARM UP 11 – 2 9

Section 3 Essential Question How do we solve a system using substitution?

Homework Clicky

Part III: HoffmaMethod… finding 2 unknowns with “Tweek” 1) “Tweek” the 1 st equation (solve if for a variable) 2)Move the ‘tweek’ to the 2 nd equation (substitute) EXAMPLE x + 2y = 18 x = 4y 4y + 2y = 18 6y = 18 6 y = 3 So…the solution is the ordered pair…(12, 3) 3)Solve the new equation 4)Substitute answer into original equations x = 4y x = 4(3) x = 12

4x = Find the 2 unknowns! y = x + 5 3x + y = 17 Step 1 look and Step 2 substitute 3x + (x + 5) = 17 Step 3 solve for ‘x’ 4 x = 3 Step 4 substitute 3 for ‘x’ in the 1 st equation – solve for y y = x + 5 y = (3, 8) 4x + 5 = 17 y = 8

Find the 2 unknowns! a = 3b – 3 7a – 2b = 17 7(3b – 3) – 2b = b = b = 2 a = 3b – 3 a = 3(2) – 3 a = 6 – 3 a = 3 21b – 21 – 2b = 17 19b – 21 = 17 (3, 2)

Find the 2 unknowns…REAL ‘Tweek’ 2x + y = 4 x + y = 2 Solve 1 for a variable y = -x + 2 Now substitute and solve for ‘x’ 2x + (-x + 2) = 4 x + 2 = 4 -2 x = 2 Pick an original equation and substitute x + y = y = 2 -2 y = 0 (2, 0) x + y = 2 -x You MUST substitute into the OTHER equation

Boys and Girls at Swift Middle School made cookies… They made 400 total…if the girls made 4 times the amount the boys did…how much did each make? Let b = # cookies boys made g = # cookies girls made b + g = 400 g = 4b b + 4b = 400 5b = b = 80 g = 4b g = 4(80) g = 320 Girls made 320 cookies Boys made 80 cookies

A little Challenge? Solve the following…for all 3 variables! r = 4t v = 7t r + v = 220 Double substitute! If r + v = 220, then 4t + 7t = t = t = 20 r = 4(20) = 80 v = 7(20) = 140

Homework Do HoffmaSheet 9 – 3